End-to-end pseudo-measurement learning for state estimation under limited observability

Distribution System State Estimation (DSSE) is becoming increasingly important with the integration of Distributed Energy Resources and the active operation of distribution networks (DNs), but it remains challenging due to the limited and heterogeneous monitoring infrastructure available in these networks. To address this challenge, this paper proposes a novel DSSE framework that restores observability through data-driven pseudo-measurements generated by a Neural Network (NN), while preserving the exact non-linear AC power flow model within a classical Weighted Least Squares (WLS) estimator. Unlike conventional approaches that generate pseudo-measurements independently of the downstream state estimation, the proposed method explicitly couples both components through an end-to-end learning formulation. Specifically, the WLS estimator is embedded as a layer within the NN architecture, enabling implicit differentiation to propagate the impact of pseudo-measurements on the final estimation error back to the NN parameters. Extensive numerical experiments on the IEEE 30-bus and IEEE 33-bus systems demonstrate that the proposed framework consistently outperforms state-of-the-art methods in state estimation (SE) accuracy under a wide range of loading conditions and measurement configurations.